Let's start by paying close attention to the terms of the given sequence.
cccc
a_1 & a_2 & a_3 & a_4
2500 & 500 & 100 & 20
To write the next three terms, we first have to find the common ratio. To do so, we will calculate the quotient between any two consecutive terms. For simplicity, we will find the quotient between the second and the first terms.
a_2/a_1=500/2500= 1/5
We have a geometric sequence with a common ratio of 15. To find the next three terms, we will multiply the value of the last term by 15 and repeat it twice.
rrrrc
a_5&=& 20 ( 1/5) &=& 4
a_6&=& 4 ( 1/5) &=& 4/5
a_7&=& 4/5 ( 1/5) &=& 4/25
To graph the first eight terms, we will let the horizontal axis represent the position of the term within the sequence — this is the domain — and the vertical axis will represent the value of the terms — the range.
